PROVE THAT THE ANGLE OF REPOSE IS EQUAL TO THE ANGLE OF FRICTION I.E. α = φ

From the condition of equilibrium

(  ͢+) Σf_x = 0

F – Wsinα = 0

F = Wsinα …………….(1)

(+↑)Σf_y = 0

R – cosα = 0

R = cosα ………………….(2)

Again F = μR

From equation (1)

F = μR = Wsinα

μ x Wcosα = Wsinα

μ = Wsinα/ Wcosα = tanα = tanφ

or α = φ

Alternatively

tanφ F/R = Wsinα/ Wcosα = tanα

Or φ = α

LAWS OF FRICTION

LAWS OF STATIC FRICTION (COLUMB’S LAW OF FRICTION)

        1.       The force of friction is always acting opposite to the direction of motion of the body.

        2.       The magnitude of the force of friction is exactly equal to the force which tends to move the body CP = F

        3.       The force of limiting friction bears a constant ratio with the normal reaction (R) between the contact surface i.e. F/R = constant = μ (co-efficient of froction)

        4.       The force of friction is independent of the area of the contact between the surface.

        5.       The frictional force depends upon the roughness of the surface in contact.

 

USEFULL AND HARMFULL EFFECTS IN FRICTION

USEFULL EFFECTS

       1.       It is impossible for every body to walk on  the road without the effects of friction.

       2.       Machineries can do useful work with the aid of friction force.

       3.       When we write something on the exercise book or black board , it is due to friction.

       4.       If we pullout nail from wood the frictional force offer.

      5.       When ladder is placed with its one end on the vertical wall and the other end at floor , the frictional forces prevent the ladder from slipping due to friction.

      6.       When we do some work by our hands , things does not slip from our hand due to frictional effect.

 

HARMFULL EFFECTS

       1.       Large amount of power has been last due to friction in engines, gears , trains , bearings etc.

        2.       Changes of wirn out of machine tools due to friction.

        3.       When a fluid run over a pipe  there is a chance of producing heat due to friction.

        4.       Heat generated due to fluid friction between air and outer surface of air –craft.

        5.       Due to frictional effects of dry leaves of a forest , changes of great firing.